Information about Europe Europa

6. Forecasting Output, Expenditure, and the Price Level

International Monetary Fund
Published Date:
November 2005
  • ShareShare
Information about Europe Europa
Show Summary Details

a. Some basic concepts

The output of goods and services in an economy is the result of combining factors of production, customarily classified as the stock of capital and labor. The former includes machinery, buildings, and infrastructure for transportation and communications. It also includes inventories of raw materials, semi-processed items, and finished goods that have not yet been sold. The volume of output depends on the degree of use of the available productive factors as well as on how efficiently they are used. The intensity of use of capital assets can be measured by the rate of capacity utilization, which is the ratio of fixed capital assets actually in use to the total stock of such capital. The intensity of labor use is measured by the ratio of labor actually employed to total labor force, or conversely by the rate of unemployment. The more efficiently a given set of factors is used, the higher the volume of output that they produce, and thus the more productive they are. The concept of total factor productivity (TFP) has been developed to help measure this technological effect on production.

A number of studies have looked into the determinants of economic growth over a wide array of countries by comparing rates of increase in capital and labor inputs with output growth. If the latter has been faster than the growth in inputs, this is attributed to rising TFP. Growth accounting studies during the postwar period have tended to ascribe the significant differences in growth rates among countries to differences in the change in total factor productivity. Since TFP is defined to be the component of growth rates not explainable by changes in labor and capital inputs, this conclusion is to a degree tautological, although the presumed basis for substantial TFP differences was the growth of technology and its absorption into a country’s installed capital stock. More recent research has cast doubt on some of the simplifying assumptions used in measuring the “quantity” of labor and capital. For example, if the proportion of skilled laborers within the labor force is rising, but the size of the overall labor force remains unchanged, this should be counted as an increase in labor. Capital is even harder to measure accurately, a matter of debate especially relevant to studies of the high growth achieved in recent decades in some East Asian economies. In addition, other aspects of the economic environment—including the quality of governance, the stability of the regulatory environment, and the adaptability of the labor force to change in the output mix—have been found to correlate strongly with TFP change. An important policy implication of the debate is as follows: If growth occurs because of a growing capital stock, then eventually growth must slow because increases in the capital stock will encounter diminishing returns. This is the main lesson of neoclassical growth theory. But if growth occurs because TFP is increasing, then long-term growth may be sustainable.

In a smoothly functioning dynamic market economy, the patterns of production respond continuously to changes in consumer preferences, changes in relative prices of inputs, and other shifts in the conditions affecting supplies and demands for various goods and services. At any moment, some resources will be shifting between various activities and may be temporarily idle. On the other hand, in times of very strong demand factors may work overtime—if prices are high enough to cover the extra costs. One can speak of a normal degree of slack in utilization of productive resources. The output level corresponding to a normal degree of slack, or intensity of resource use, is called potential output. The actual level of output, and income, can be below the potential level, if for some reason there is a high degree of unemployment of labor and underutilization of the capital stock. Productive factors may also be employed in quantities exceeding their normal intensities for a limited period of time, pushing total output beyond its long-term potential. The concept of potential output is basically a technical relationship between inputs and output, which has been analyzed and estimated using various forms of a production function. This relationship specifies the aggregate supply of goods and services given the nation’s endowment of productive factors and the prices for inputs and outputs. The level of aggregate demand, on the other hand, is the level of expenditure on current production that economic agents are willing to undertake. If the level of demand is less than potential output, either the average price of output will fall or the quantity produced will decline, or some combination of the two will take place. If, on the other hand, the level of expenditure exceeds potential output, there is upward pressure on the price level, and the quantity of output will be pushed above potential. Prices of goods and services will tend to rise, or the current inflation rate will accelerate. It is commonly assumed that deviations of actual from potential output are caused by demand conditions although temporary disruptions on the supply side may also be involved.

b. Forecasting output and expenditure

Techniques for forecasting output and expenditure—and prices, for that matter—should be based on an explicit framework for analyzing macroeconomic developments. Such a framework specifies that output and prices are determined through the interplay of aggregate supply and demand. An aggregate demand function relates total expenditures to variables such as incomes, output prices, interest rates, and public sector policies. An aggregate supply function would also include output prices and input prices as explanatory variables. Ideally, a forecasting model would use projected values of the explanatory variables to solve for the equilibrium between aggregate supply and demand, which would yield values for output and prices for a future period. Complexities and problems involved with such modeling, including data requirements, make it impracticable in some cases, however, and it is necessary to use simpler and more intuitive methods to produce the forecasts. These include forecasts based on specific developments affecting individual sectors—such as agriculture, manufacturing and services—using relationships among sectors to get an estimate of aggregate output. An alternative is to use trend projections of potential output as a benchmark to which the effects of changes in policies can be related. Given the special situation faced by Turkey in the mid-1990s, this latter approach may prove quite useful.

(1) Potential output

The level of potential output can be estimated using methods of varying sophistication. Ideally, one would estimate a production function in which output depends on capital and labor inputs as well as TFP, and establish levels of “normal” intensity in factor use. Reliable data on the capital stock and labor force are a prerequisite for this approach. If, as is the case with most non-OECD countries, such data are not available, simpler techniques have to be used. One possibility is to assume that potential output grows at rates more or less close to a long-term trend as determined by the growth of inputs and technological progress. Expansionary policies or exogenous increases in demand may increase output growth temporarily; contractionary policies or reductions in demand may decrease it. However, over time there will be some tendency for the actual growth rate to move into line with the longer-run growth of potential supply. If the period over which the average actual rate is computed includes a “typical” balance between expansionary and contractionary years and positive and negative shocks (weather fluctuations, military conflict, labor strikes, baby booms, scientific discoveries) and no major introduction or reform of structural distortions, then the historical average of actual rates will tend to equal the potential growth of output.

(2) Expenditure

Projections of domestic expenditure have to take into account the decomposition of the total into consumption and investment, as well as a further division of the two into components undertaken by the private and government sectors. Private sector consumption (and its obverse, saving) and investment behavior have been studied extensively for a wide variety of countries, and the results of this work provide a good basis for forecasting. Public sector behavior, on the other hand, is to a large extent a matter of policy. Therefore, forecasts relating to this spending category have to rely on indications of intended policy actions, such as the relevant budgetary projections.

Private consumption

Economic theory relates private consumption to (i) the level of private disposable income, (ii) interest rates, (iii) expected inflation (which reflects the relative price between current and future consumption), and (iv) sometimes to other factors such as the distribution of income or changes in income (permanent and transitory components of income).

Household disposable income (YD) can be viewed from the standpoint of either its sources or its uses:

where variables are defined as follows:

Y: wages, salaries and other household incomes;

T: taxes less transfers; that is, direct personal taxes, such as the income tax, net of personal transfers, such as pension receipts and unemployment insurance benefits;

CP: private consumption;

SP: private savings.

Equation (6.1) shows that household consumption and household savings are simultaneously determined. For a given level of disposable income, once private consumption is known, household savings is determined as a residual.

In addition to the accounting link between household consumption and household disposable income, economic theory postulates a behavioral relationship between the two. Expressed in real terms, a simple form of this relation is

This specification of the consumption function implies that the marginal propensity to consume (MPC, or Δ CPR/ΔYDR) is constant and is equal to b, while the average propensity to consume (CPR/YDR) falls as YDR increases, due to the declining relative importance of a positive constant term. These properties suggest that developments in consumption and savings will help stabilize the economy because the savings ratio tends to rise in booms and decline in slumps. Further, as income grows over time, they suggest a long-term rise in the savings ratio.

The above simple consumption relation could incorporate more explanatory variables to make it consistent with the “permanent-income” explanation of household consumption. A more complete consumption function could be written as follows:

where the variables are defined as follows:

CPR: private consumption expenditure in constant prices;

YDRe: a measure of current and expected future household disposable income in constant prices;

NWR: net real wealth of households;

r: the real after tax interest rate;

Z: other potential explanatory variables.


Gross investment, or gross capital formation, includes spending on machinery, equipment and structures, and changes in inventories. For forecasting investment in market economies, it is useful to distinguish between government and private investment. Projections of government investment should be consistent with budget plans. In countries in transition, the investment projects of state-owned enterprises are also a major concern of the political authorities. As a consequence, the behavior of investment by public enterprises may not be determined solely by market-related forces.

For private business investment, theoretical models focus on the rate of return and the cost of finance to the investor. However, investors’ expectations of future sales may well dominate their rate-of-return calculations. Investor confidence and expectations generally contain a large element of judgment that is difficult to quantify. It may be possible to proxy investors’ expectations with past changes in actual output. (The hypothesis that the desired capital stock, and therefore investment spending, tend to vary with changes in output is sometimes referred to as the “accelerator model.”) Besides past changes in output, real investment is likely to respond to some measure of the cost of funds, such as real interest rates. Third, inflation may deter investors because it is symptomatic of an uncertain business environment; investors may prefer to wait to risk their funds until the probability of an attractive return is higher. A high rate of inflation, or a large increase in the rate, is likely to be associated with lower investment spending. Finally, investment projects will be more profitable the lower is the real exchange rate (other things being equal). This means that a lower rate will tend to be associated with a higher level of capital formation. This is logical, however, only if investors think that a change in the exchange rate is likely to be lasting; if they are accustomed to recurring fluctuations in the real rate, it is rational for them to discount or ignore changes.

Net investment means spending on capital goods that constitute an addition to production capacity that existed before. For fixed investment (investment excluding inventory changes), net investment is calculated as “gross” investment (all new plant and equipment) less depreciation (an estimate of the amount of the capital stock that is used up or worn out during the period). It is net investment that varies with the change in real GDP according to the accelerator model. The part of gross investment that replaces or maintains the existing capital stock is likely to be proportional to the existing capital stock, and therefore proportional to real GDP as a first approximation. That is, part of gross investment varies with the change in GDP, and part with the past level. One may summarize these hypotheses in the expression

where the variables are defined as follows:

FIR:fixed investment in real terms;

YR: GDP in real terms;

r: the real interest rate (the nominal rate adjusted for the rate of inflation);

∏: the rate of inflation;

ER: the level of the real exchange rate.

Some studies have emphasized that the availability rather than the cost of finance represents a major constraint on private investment. This may reflect the maintenance of real interest rates at below market levels and the rationing of financial resources by non-price means. In this case, bank credit, foreign capital inflows, and retained profits represent the major determinants of private investment. The availability of bank credit reflects the stance of monetary policy. Fiscal policy is also important to the extent that there is a possibility of financial crowding-out. This occurs when there is a large demand by the government for credit from the banking system, limiting its availability to the private sector.

c. Forecasting output and expenditure in Turkey

(1) Potential output

The purpose of this section is to provide a guide to making a projection of potential output for Turkey in 1996. As data for capital stock are not available and the statistics for employment are incomplete, based primarily on large enterprises, direct estimation of potential output through use of a production function is not feasible. Consequently, we have to use information that is available to form a judgment about the level of potential output in 1996.

Estimation of a time trend for real GDP for the period 1984-95 gives the following regression equation:

R2 = 0.96 SEE =.03298 D.W. = 1.86 1984-95

where the variables are defined as follows:1

LGDPR: natural log of real GDP (GDP in constant 1987 prices);2TREND: time trend = 1 in 1970, 2 in 1971, and so forth.

Actual and predicted values, derived by taking antilogs, are shown in the data appendix (“GDPR and “TRENGDPR”). There are particularly large, positive residuals in 1987 and 1993, smaller positive residuals in 1990 and 1992, suggesting that output was above potential in those years, and below potential in, for example, 1994 and 1995.3

Table 6.6 shows evidence on intensity of resource use in Turkey in recent years. As already mentioned, the figures for employment are not comprehensive, and caution should be used in drawing conclusions from them. The data for capacity utilization cover only the most recent period, thus being of limited use at present in quantitative analysis. However, both sets of data can be used as evidence in assessing informally whether the level of real GDP of a given year is high or low in relation to potential output.

(2) Private consumption

Estimates of a consumption function are given in Table 6.1.4 While longer time series exist, the sample for estimation was 1981 -95 for each equation because of the major reforms undertaken in 1979-80 5. (Comparative regression results with alternative sample lengths tend to confirm this choice.) Actual and predicted values are shown in Table 6.2.

Figure 6.1 TurkeyTurkey: Real GDP, 1984-1995

(In billions of liras, 1987 prices)

The first equation in Table 6.1 is a naive model, based only on trend. It is noteworthy that, with no “explanatory” variable other than trend, the R2 is as high as 0.95. A log-linear trend (not shown in Table 6.1) does not perform better than the linear trend (equation (6.6)) judging by the correlation coefficients. This pattern for log transformations recurs throughout the other specifications of the consumption function that were fitted. Since, in the case of this relationship, taking logs did not result in a better fit in any of the cases tried, only one log specification is presented in Table 6.1.

A consumption function with GDP as the explanatory variable (equation (6.7)) performs somewhat better than trend; the standard error is about 10 percent smaller. The improvement comes about because in years in which GDPR departs relatively more from trend, a simple structural model such as equation (6.7) predicts CPR better than the naive model. This is shown in Figure 6.2. The overall level of explanation is not appreciably greater as measured by the R2’s. The main differences between equations (6.6) and (6.7) are the drop of about 10 percent in the standard error and the much smaller Durbin-Watson statistic (DW) in the latter case, denoting autocorrelated error terms in the structural model. Since changing the form of the equation from linear to log-linear did not affect the DW in this case, it is logical to suspect a missing variable or other specification error. In equation (6.8), the lagged value of the dependent variable is included in the specification, but its coefficient is not significant. (It is also insignificant in other specifications, to be reported below.) This leads one to rule out a missing simple lag structure as the explanation for the poor Durbin-Watson.6

Two other hypotheses were tested. In the first, the specification was changed to allow for the possibility that Turkish consumers spend a different proportion of trend income on consumer goods than they spend out of fluctuations in their income. The strong stop-go pattern in aggregate demand policy in Turkey can be expected to cause uncertainty among consumers regarding whether a change in income is permanent or temporary. Results are shown in equation (6.9). This hypothesis receives only weak support from the data, although in subsequent specifications, it tends to be confirmed. (The possibility of a smaller marginal propensity to consume out of “temporary” income changes was also modeled using trend GDPR and deviations from trend, but the standard error of the equation was higher; these results are not presented.)

Table 6.1.Turkey: Regression Estimates for Forecasting Private Consumption 1/
Equation NumberDependent VariableConstantTRENDLaggedDependent VariableGDPRΔGDPRINTCPRDUMR2DurbinWatson StatisticStandard; Error
(6.7)CPR12.4470.54500 960.91,739
(6.12)LCPR 2/1.61350.78540.35090.1236-0.07790.992.50.016

The sample for estimation in each case is 1981-95. Figures in parentheses are t- values. Definitions of variables are given below (see also the data appendix in the last section of this volume): TRENGDPR: defined by equation (5) of this workshop;


Explanatory variables are also in log form (except CPRDUM: ΔGDPR is ΔLGDPR).

The sample for estimation in each case is 1981-95. Figures in parentheses are t- values. Definitions of variables are given below (see also the data appendix in the last section of this volume): TRENGDPR: defined by equation (5) of this workshop;


Explanatory variables are also in log form (except CPRDUM: ΔGDPR is ΔLGDPR).

Table 6.2.Turkey: Actual and Predicted Values of Private Consumption
ActualFitted CPR
YearCPREq. 6.6Eq. 6.7Eq. 6.8Eq. 6.9Eq. 6.10Eq. 6.11Eq. 6.12

Figure 6.2 TurkeyPrivate Consumption

(In billions of liras at 1987 prices)

The second hypothesis is that GDPR is a poor measure of household disposable income. GDPR is used here as a proxy because data for disposable income are not available. To calculate household disposable income, one would need time series for GDP, depreciation, and aggregate government revenue (all available), plus payments of net transfers by government to nongovernment. This last-named series, which contains social insurance benefits as well as subsidies to enterprises, is not available on a consistent basis. Perhaps more important, a significant component of disposable income is interest receipts. Interest rates have been very high in Turkey in recent years (much less so earlier), they move contra-cyclically, and interest income has not been taxed in recent years.7 For all these reasons, it is likely that GDP alone is an imperfect proxy for household disposable income (explaining why the structural models do little better than the naive models and the DWs are so much worse). As a proxy for the “missing variable” of interest income, a nominal three-month interest rate is included in the specification in equations (6.10) and (6.11). The sign on the coefficient of this term is appropriately positive, the opposite of the theoretical substitution effect,8 and the results are very strong. The R2’s increase substantially relative to the naive model, and the evidence of autocorrelation virtually disappears.9 The negative effect of the compulsory savings scheme (instituted in 1987) on consumer spending receives moderate support (equation (6.11)).

(3) Gross fixed investment

Alternative estimates of an investment equation are given in Table 6.3, and actual and predicted values are shown in Table 6.4. The first two rows of Table 6.3 show results for naive models. The use of trend as the only right-hand-side variable yields an R2 of 0.91 (equation (6.13)); trend plus the lagged endogenous variable achieves 0.92 (equation (6.14)). Investment is usually hard to explain and predict because of the importance of unobservable expectational or confidence factors.

Table 6.3.Turkey: Regression Estimates for Forecasting Fixed Investment 1/
Equation NumberDependent VariableConstantLagged Dependent VariableΔ GDPRGDPR(-1)RINT(-1)RERA(-1)INFLPGDP(-1)TRENDFCAPR2R2Durhiri WatsonStandard ErrorSample
(6.17)FIR-14,0970.4451 2/-97.34-42.910.27850.992.1897.61979-95
(6.19)LFTR 3/-13.7012-57322.1055-0.008343-0.0040800.982.40.061031979-95

Figures in parentheses are t-values. Definitions of derived variables are given below:

RINT: 100 * ((1 + INT/100)/(PGDP/PGDP(-1)) - 1);

INFLPGDP: 100*(PGDP/PGDP(-1)-1);

RERA: (NERM/(857.2 * 3.776))/ (PGDP/ICPGDP);

FCAPR: FABAL_D * (NERA/1000)/PGDP; regressor FCAPR2 is sum of current and lagged values.

Coefficient on unlagged GDPR, as explained in text.

Explanatory variables (except the real rate of interest and the inflation rate) are also in logs: the difference of the log of GDPR for ΔGDPR, and the lag of the log of GDPR for GDPR (-1).

Figures in parentheses are t-values. Definitions of derived variables are given below:

RINT: 100 * ((1 + INT/100)/(PGDP/PGDP(-1)) - 1);

INFLPGDP: 100*(PGDP/PGDP(-1)-1);

RERA: (NERM/(857.2 * 3.776))/ (PGDP/ICPGDP);

FCAPR: FABAL_D * (NERA/1000)/PGDP; regressor FCAPR2 is sum of current and lagged values.

Coefficient on unlagged GDPR, as explained in text.

Explanatory variables (except the real rate of interest and the inflation rate) are also in logs: the difference of the log of GDPR for ΔGDPR, and the lag of the log of GDPR for GDPR (-1).

Table 6.4.Turkey: Actual and Predicted Values of Fixed Investment
ActualFitted FIRActualPredicted
YearFIREq.(6.13)Eq. (6.14)Eq. (6.15)Eq.(6.16)Eq. (6.17)Eq.(6.19)FIPRFIPR(6.18)

The results for the basic accelerator model are given in equation (6.15) in Table 6.3. Here the lagged value of FIR is used to represent the influences of lags of all right-hand variables, and the equation does not include additional lagged values of ΔGDPR. A version of the investment function including variables representing the real interest rate, the inflation rate, and the inflow of foreign finance appears on the following line, equation (6.16).

The sample length is 1979-95. Structural reforms undertaken in the early 1980s do not affect the investment relationship according to a comparison of results obtained from data samples including and excluding these years.

The coefficients on the variables ΔGDPR and GDPRt-1 are roughly equal in equation (6.16). That means that statistically these two variables may be replaced by unlagged, undifferenced GDPR, a simpler specification. While such a change may be defensible statistically (the two forms are said to be “observationally equivalent”), it is not logical for investment to be driven by GDPR, and the interpretation based on the two terms, ΔGDPR and GDPRt-1, is more likely to be correct. Nevertheless, for ease of forecasting, the simpler specification is shown in equation (6.17).

Two additional versions of the investment function are given in Table 6.3. In equation (6.18), the model is estimated with data adjusted to exclude general government expenditure on investment.10 While the coefficients are not exactly the same size, the two equations are generally similar. The R2 for private investment by itself is still quite high. The real interest rate and the inflation rate explain better in the equation for total fixed investment, and the real exchange rate does better for private investment alone; there are no obvious theoretical reasons why this should be so.11 There does not appear to be any econometric reason not to use specifications based on total fixed investment.

Equation (6.19) gives results for the specification estimated in logs. (Note that variables taking on some negative values are left in their original form; only FIR and GDPR are transformed by substituting logs.) For equation (6.19), the coefficients may be interpreted as elasticities or semi-elasticities. For example, for the coefficient on GDPR(-1), an increase of x percent in real output in period t will tend to be associated with an increase in real investment spending of approximately 2x percent in period t+1; for the depreciation hypothesis to be borne out, an elasticity on lagged output of two is on the high side. The elasticity on the unlagged change in output is about ; since investment is about one fifth of GDP, the implied incremental capital-output ratio is approximately unity, which is low.

d. Determinants of the average level of prices

The framework of aggregate supply and demand can be used to analyze the behavior of the price level as well as output. The supply of goods and services can be expected to respond positively to higher prices, and the quantity demanded will decline with a rising level of prices. Simultaneously, the price level is affected by factors working through supply and demand. On the supply side, factors influencing price (also called cost push factors) include wages, world market prices of imported inputs, indirect taxes, and government administered prices. Factors causing demand to expand will, other things equal, also put pressure on prices, a phenomenon referred to as demand pull. Fiscal and monetary policies are of central importance in this regard, especially to the extent that they result in monetary expansion. The private sector can also change its demand patterns autonomously, for example in response to changed expectations. Expectations of future price developments have come to take a central place in inflation analysis and forecasting, as they also affect the cost side factors; wage increases incorporated in labor contracts are likely to rise if inflation is expected to be high. A major difficulty with including expectations in empirical analysis and forecasting is that they are not observable directly and, therefore, difficult to measure. Expectations may be represented by past actual values (of inflation, for example), as a proxy for expected values.

e. Forecasting the price level in Turkey

The starting point of the forecasting techniques used in this section is the interplay between aggregate supply and aggregate demand discussed in the preceding section. A simple model can be constructed along the following lines: Real aggregate demand is specified to increase when the real money stock rises and when competitiveness improves (domestic prices of exports decline relative to foreign prices of competing exports). Aggregate supply, on the other hand, declines if real wages or prices of imported inputs rise. The domestic prices of exports and imports are the products of world market prices in foreign currency and the exchange rate. Solving for the equilibrium between aggregate supply and demand allows us to express the long run price level as a function of the exchange rate, the money supply, wages, the average world market price of exports, and the average price of imported inputs.

where variables are defined as follows:

P: average level of prices;

E: nominal exchange rate (Turkish liras per unit of foreign currency);

MS: money supply;

W: average nominal wage rate;

PX.E: world market price of exports in domestic currency;

PM.E: world market price of imports in domestic currency.

Increases in MS, PX and PM tend to raise the price level whereas appreciation of the domestic currency (a fall in E) would lower it.

In reality, two aspects of the price-determining mechanism complicate this supply-demand picture. One is simultaneity. A depreciation of the currency will tend to result in further increases in the price level, but higher prices will also tend to promote an exchange rate adjustment, to preserve competitiveness. Similarly, wage increases normally lead to price increases, and a higher cost of living stimulates demands for higher nominal wages. The second complication is lags. An increase in the fiscal deficit may lead promptly to more demand pressure, subsequently to an increase in the money supply (if the deficit financing has monetary implications), eventually to an increase in nominal production costs and prices of domestic output (as inflationary pressures spread through the productive sector), and ultimately to an increase in import prices (as the currency depreciates to equilibrate the foreign exchange market) and to higher nominal wages. These feedback effects, which have their own lag structures, will in general strongly affect the econometric results obtainable from single-equation model specifications.

Two alternative price-forecasting methods are proposed below. Both involve some simplification of the simultaneity that in reality occurs in the determination of prices. In the first method, the forecasting procedure is as follows: Start with the assumption that the rate of inflation is itself sticky downward—if inflation was 50 percent in the final historical year, it is more plausible to assume it will be 50 percent in the forecast year than to assume it will be zero in the forecast year. Next, identify exogenous factors that will tend to increase or decrease the rate relative to what was observed in the last historical year. The main items to be taken into account are acceleration or deceleration of export and import prices (export prices to forecast the GDP deflator, import prices to forecast the consumer price index, CPI), changes in indirect taxes, known changes in administered prices, and disturbances from the global environment (weather, military conflict). Finally, make a judgmental addition or subtraction for the expected effects of the stance of monetary and fiscal policies in the forecast year.

In some cases the effects of exogenous changes (for example, changes in export and import prices) can be quantified, but in others, judgment must be used. If import prices in domestic currency rose 50 percent in year t, and are forecast to increase a further 50 percent in year t+1, and if inflation (measured by the CPI) in the economy was 50 percent in year t, then the forecast change in import prices for year t+1 does not have any tendency to speed up or slow down the inflationary momentum that existed in the economy at the end of year t. If the forecast of import prices for t+1 is, however, 70 percent (including changes in world market prices and changes in the lira exchange rate), following 50 percent the year before, this will tend to increase the economy-wide inflation rate in year t+1. Since the share of imports (goods and services) in total GDP is about one quarter for Turkey (26.6 percent in Table 6.7 in 1995), the direct inflationary effect of the hypothetical increase in foreign prices would be about 5 percentage points—one quarter of (70-50). That is, holding everything else constant, the domestic inflation rate as measured by the CPI will increase by about 5 percentage points, to 55 percent, if the increase in foreign prices in domestic currency accelerated from 50 percent to 70 percent. Similar calculations may be performed for export prices (which affect the GDP deflator), and for wage rates. (Recorded wages and salaries account for 25-60 percent of value added in Turkey; see Section e in Chapter 1.)

One may define a “neutral” fiscal policy stance to mean one that will not add to or subtract from the relative amount of aggregate demand in the economy, so that the inflation rate will tend neither to speed up nor to slow down on account of fiscal stimulus in the forecast year, other things being equal. If monetary policy is neutral, this can similarly be interpreted to mean, in the context of the first method, that it will not exert an independent influence on the inflation rate in either direction (inflationary or deflationary shocks on the supply side will be accommodated). If monetary policy is tightened, a shortage of liquidity will tend to raise interest rates and inhibit spending until money demand is forced into line with money supply—monetary tightening will tend to reduce the inflation rate. The quantitative link between the degree of fiscal and/or monetary tightening and a change in the short-run inflation rate is left to judgment.

The second approach to forecasting the price level relies on statistical patterns from past years, a single-equation model containing both demand-side and supply-side influences on prices. It employs the assumption that these influences occur in a definite sequence; in particular, it assumes that changes in the money supply in period t result in changes in the price level in period t+1. Thus, the simplification involved in the first method is that it did not rely on a formal, quantified link between the inflation forecast and the stance of monetary policy that is consistent with it; that was accomplished through judgment. The second method does quantify this relationship; the equations below are provided for that purpose. However, the second method assumes that only last period’s money affects this period’s price changes. While there does tend to be some lag, the simplification rules out any contemporaneous relation between money growth and price increase. In doing so, it avoids simultaneity issues and any inconsistency with the money demand equation in the monetary forecasting workshop, which makes demand for money depend on the price level of the same period, and with the method introduced below for determining the nominal exchange rate. In cases in which the assumption may be unsatisfactory (a speed-up in monetary growth in the last historical year), the forecast may be adjusted on a judgmental basis.

The first of the three equations presented below specifies the level of the CPI to depend on the average level of wages, on import prices, and on the money stock lagged one period. The second substitutes the fiscal deficit (public sector borrowing requirement) for money growth, in reflection of the hypothesis that it is government borrowing that is responsible in large part for the rapid growth in liquidity. (In the second equation, the fiscal deficit is hardly significant at all if the wage variable is included in the equation.) The third equation admits both fiscal and monetary sources for inflation, and indicates a somewhat independent role for each. Part of money growth may be related to capital inflows or to expansion of credit to the private sector, and not solely to government borrowing. A fiscal deficit may stimulate inflation in the short run by adding to demand and fostering market shortages, to some degree independent of monetary expansion. Except for varying Durbin-Watson statistics, all three equations exhibit generally robust econometric properties, although the two including the money-stock variable are superior judged by the standard errors. (The R2’s range from 0.9996 to 0.9999.)

Let L denote natural logarithms, and let the variables be defined as follows:

CPI: consumer price index (1990 = 100);

PM: the average level of import prices in liras (PM_D*NERA/521.07; PM = 100 on average in 1984–86);12

WAGE: wages and salaries in billions of liras;

AM2X: the average stock of broad money (including foreign-currency-denominated deposits), the mean of two successive end-year values, in trillions of liras;

PSBR: the public sector borrowing requirement in billions of liras.

R2 = 0.99+ SEE = 0.02494 D.W. = 2.2 1984–95

R = 0.99+ SEE = 0.04383 D.W. = 1.1 1984-95

R2 = 0.99+ SEE = 0.02004 D.W. = 2.7 1984-95

Actual and predicted values for the level of the CPI are given in Table 6.5. A method for estimating the level at the end of the forecast year is explained in Appendix II.

Table 6.5.Turkey: Actual and Predicted Values of the Consumer Price Index, 1984-95(Index = 100 in 1990)
CPIFitted Values
ActualEq. (6.22)Eq. (6.23)Eq. (6.24)

f. Forecasting a consistent set of national accounts deflators

In a typical forecasting exercise, either the GDP deflator and/or the CPI will be determined at an early step in the process, perhaps tentatively, based on the outlook for inflation in the forecast period. The forecast changes in the prices of exports and imports of goods and services will probably be available beforehand, based on published forecasts of an international organization (discussed in Chapter 8, below). The purpose of this section is to present a simple algebraic framework for determining the deflators for the remaining components in a way that is consistent with the forecast values of the GDP deflator, the CPI, and foreign trade price indices. The algebra is developed for this case in particular but may easily be modified to accommodate more, or less, information.

The accounting identity equating nominal GDP in period t to the sum of types of spending may be written,

The above expression has been tailored to fit the case of Turkey. Consumption goods produced by government and consumption by the private sector are shown separately, but investment includes both private and government. Exports and imports include both goods and services, as is usual in the national accounts. The statistical discrepancy has been combined with investment.

Dividing both sides of equation (6.23) by GDPRt (where R denotes output or spending in real terms), one obtains

The terms on the right-hand side may be decomposed into two factors, as follows:

On the right-hand side of equation (6.25), one of the factors in each term is the share of the component in total GDPR, and the other factor is the level of the deflator for that term (Strictly speaking, it would be the level of the deflator if multiplied by 100.) To simplify notation, let the share of spending in real GDP be denoted swwt where ww denotes a specific component of spending, and let P represent the level of the corresponding deflator. With this notation, the expression can be rewritten,

Now define szt as the combined share of all spending components for which no deflator has as yet been forecast, and PZ as the unknown deflator of this combined category. After substituting szt • PZt for the terms in I and CG above, the resulting expression could be solved for PZt if the shares were known. Since shares of GDP are likely to change little from year to year, values of shares from the preceding year may be used (t being the forecast year), and the expression will still hold approximately.13

It is useful to carry the algebra one step further. If the base year of the national accounts happened to be t-1, or if the levels of the deflator series were adjusted so that this were true, then each of the P terms in equation (6.26) would equal unity plus the change in the deflator expressed as a fraction. For example, for the left-hand side of the equation, this ratio would be equal to one plus the change in the GDP deflator from t-1 to t; in symbols,

where II refers to the percentage change in a deflator. Since the sum of the shares is unity, we may subtract unity from both sides of equation (6.26) and multiply by 100, to obtain

which can be manipulated in much the same way as equation (6.26), to yield an estimate of the change in the unknown deflator that is consistent with values of known changes in deflators. In this case, the Π’s may be interpreted as year-on-year changes in the deflators, and the expression is written as an approximation because values of shares from the preceding year are used instead of values from year t.

There is one point to bear in mind when interpreting equations (6.26) and (6.28): These two expressions look very much like weighted averages; the shares must sum to one. It might appear that the change in the GDP deflator, on the left-hand side, would lie in the range defined by the largest and smallest changes in component deflators on the right-hand side. However, the import term has a minus sign, and therefore this familiar characteristic of weighted averages does not necessarily apply. Rather, the two fundamental price-level changes are imports and domestic output (GDP). All other spending components are combinations of domestic and foreign output. Therefore, the changes in the deflators of other components (except exports14) will tend to lie within a range defined by the changes in PGDP and PM except for errors or statistical anomalies.15 (For Turkey in 1995, the changes in both the CPI and the consumption deflator lie outside this logical range.)

g. Exercises and issues for discussion

  • (1) Based on information presented in Section a through c, above, assess the level of actual output in 1993–95 in relation to potential output. Using your assessment, project potential output for 1996.
  • (2) Based on an assumption of unchanged policies (relative to 1995), make a judgmental forecast of the rate of growth of actual output for 1996.
  • (3) Obtain projections of expenditure on private consumption and total investment for the 1996 “Sectoral forecast” column of Table 6.7. Choosing from the equations presented in Tables 6.1 and 6.3, or using other methods, derive forecasts based on your group’s tentative baseline forecast for output (real GDP) or the hypothetical values provided below.
    • The real interest rate does not change relative to 1995.
    • Real GDP increases by 5 percent.
    • The real net capital inflow remains unchanged in 1996 at TL 2,809 billions in 1987 prices. (See FCAPR, in the data appendix at the end of this volume.)
  • (4) Use either the first or second method to make a forecast of inflation in 1996. If you use one of equations (6.20) to (6.22), what criteria do you use in choosing among them? You may make the following assumptions concerning percentage changes for the values of the explanatory variables in 1996, or use other values if you have already forecast these variables independently:
    • Import prices in U.S. dollars change by -0.5 percent (see Table 8.13).
    • The lira depreciates with respect to the U.S. dollar so that the average rate goes from lira 45,845 per dollar in 1995 to 80,000 per dollar in 1996.
    • The wage rate rises by 90 percent.
    • The PSBR is 7.5 percent of GDP. To convert this percentage to liras, use the forecast of real GDP obtained above in exercise (2) and a trial value for the rate of change of the GDP deflator (for example, the change from 1995). Iterate as appropriate.
    • The price of imports in liras declines by 1.1 percent because of tariff reductions made at the beginning of 1996 in anticipation of joining the European Union.
  • (5) During the three months or so before national parlimentary elections at end-1995, it is said that state economic enterprises postponed price increases in order to create a more favorable political climate for the incumbent party. Assuming this is correct, make a rough estimate of the extra inflation to be expected in 1996 if SEEs allowed their prices to “catch up” as soon as the elections are over.
  • To do this, one would need to know the share of SEEs’ output in GDP, which is around one eighth (see Part I). Let X be the true, unobserved, underlying rate of inflation in 1995. Observed inflation will be a weighted average of the output prices of non-SEEs (weight = 7/8) and SEEs (1/8). Prices for non-SEE producers went up at the rate of X percent throughout 1995, whereas prices for SEEs went up by X percent only during the first three quarters of 1995. Observed inflation therefore is given by (7/8)(X) + (1/8)(3/4) X= 88 percent.
  • Is it appropriate to use your estimate of suppressed inflation to modify your inflation forecasts for 1996? For Method I only, or also for Method II?
  • (6) Revise your inflation forecast from exercise (5) to incorporate the assumption of an unchanged real exchange rate in 1996. While several interpretations can be given to the concept of an unchanged real rate, for this exercise assume that the real rate is unchanged on average (on a period-average basis), “real” is defined relative to changes in the CPI in Turkey, and trading partners’ price developments are as given in Table 8.13.
  • Since the exchange rate influences the forecast of the CPI in any of the methods discussed above, and the CPI will determine the nominal exchange rate corresponding to an unchanged real rate, there is a problem of simultaneity. You can simply write out the two appropriate equations and solve them simultaneously, or use an iterative method. In the second case, it would be reasonable to start with a rate of 80,000 (liras per dollar, suggested in exercise (5), above) and the CPI forecast resulting from that exercise. You can then calculate a new nominal exchange rate. If p is the rate of change in the CPI expressed as a fraction, the new nominal exchange rate (period average) is given by (45,845)(1+p)/(1+p*), where p* is the rate of change of price level of trading-partner countries on average (see Table 8.13). This value, in turn, can be inserted into the inflation forecasting method used in exercise (5) to produce a revised inflation forecast, then a revised exchange rate estimate, and so on, until successive values change by insignificant amounts.
  • (7) Forecast change in the GDP deflator for 1996 on a judgmental basis allowing for your forecast of the change in the CPI.16 What factors influence whether these two rates of change are equal or not? You might reason that, whatever their values in 1995, the two rates will move toward a logical allignment as time passes.
  • Then use these values to derive the change in the deflator for the sum of government consumption, total investment, the change in inventories, and the statistical discrepancy.
  • (8) Describe channels through which exchange rate movements might affect inflation.
Table 6.6.Turkey: Selected Indicators of Resource Use, 1991-95
Percentage change in GDP1.05.98.1-5.57.3
Rate of unemployment plus
Underemployment 1/14.815.814.616.313.6
Labor force:
Millions of people20.520.720.821.421.9
Percentage change4.
Rate of capacity utilization
in manufacturing:
Private sector73.075.779.770.977.8
Public sector77.277.779.178.180.5
Source: IMF, Turkey—Recent Economic Developments, November 1996.

Figures for 1994-95 are averages for April and October.

Source: IMF, Turkey—Recent Economic Developments, November 1996.

Figures for 1994-95 are averages for April and October.

Table 6.7.Turkey: Components of Aggregate Demand, 1993-95(In trillions of liras, at constant 1987 prices)
Gross fixed investment28.624.026.0
Changes in stocks1.5-2.91.4
Total domestic demand103.390.5102.0
Exports of goods and services17.520.121.5
Imports of goods and services-25.7-20.1-26.1
Statistical discrepancy1.50.80.6
Gross domestic product96.691.398.0
Source: OECD National Accounts.
Source: OECD National Accounts.
Table 6.8.Turkey: Components of Aggregate Demand, 1993-95(In trillions of liras, at current prices)
Gross fixed investment505.9946.21,786.3
Changes in stocks21.6-121.43.8
Total domestic demand2,116.73,841.28,026.9
Exports of goods and services271.0826.41,532.4
Imports of goods and services-383.4-788.5-1,888.0
Statistical Discrepancy-22.4-10.7-116.5
Gross Domestic Product1,981.93,868.47,554.8
Net factor income from abroad 1/15.519.592.4
Gross national disposable income 1/1,997.43,887.97,647.2
Source: OECD National Accounts and IMF, Turkey--Recent Economic Developments, 1996.

Turkey does not report foreign transfers separate from foreign income. As a result, gross national product and gross national disposable income are equal in the Turkish national accounts.

Source: OECD National Accounts and IMF, Turkey--Recent Economic Developments, 1996.

Turkey does not report foreign transfers separate from foreign income. As a result, gross national product and gross national disposable income are equal in the Turkish national accounts.


A Consumption Function for Turkey with Interest as an Exogenous Variable

The specification used in equations (6.10) and (6.11) can be motivated as follows. Write household income (“private sector” income) as the sum of interest income, YPi, and non-interest (“wage”) income, YPw,

Let t be the average rate of taxation on non-interest income. Disposable income is therefore,

Finally, assume that non-interest income is a constant proportion, α, of GDP less YPi.

where β = α (1 - t). After deflating,

We allow the marginal propensity to consume (MPC) out of the two types of income to differ. Let the MPC for interest income be given by mi, and for non-interest income by mw. The consumption function could be written

Interest income is equal to the average nominal interest rate, INT, times the nominal debt stock, D,

On the assumption that the debt stock grows in line approximately with the price level, real interest income is proxied by the nominal interest rate,

as specified in equations (6.10) and (6.11).


Estimating the Average-Period Rate of Change of the Price Level

Typically the officials of the statistical agency collect data for prices of the items in a price index throughout the month. In each successive month they collect information on approximately the same set of prices, working from the beginning of the period to the end. Strictly speaking, therefore, the weighted average of the price data that they collect refers to about the mid-point of the month if price changes occur uniformly or randomly within a typical one-month time period. Economists regard the December level of the consumer price index as the “end-of-year” level, which is sufficiently accurate as an approximation. (End-of-period banking data are usually from the last Wednesday or Friday of the month,1 and exchange-rate data from the last business day.) The average level of prices for the year is simply equal to the average of the 12 monthly index levels.2

The yearly average level of prices is appropriate for deflating yearly spending or income flows (such as wages received, consumption spending, saving, and so forth) since the deflator is representative of the period in which the flow occurred. The end-period price level is not appropriate for deflating such flows, nor is the average-period price level appropriate for deflating data for the stock of money at end-period. (The discussion of seigniorage, in Chapter 2, illustrates this point.3) In practice the end-year price level as measured by the December index value is used for deflating end-year stocks. The average-year price level and is used for deflating annual flows.

A technical question arises if one needs to approximate the annual average price level from end-year values. This would occur in the context of forecasting if the annual average inflation rate is included in the items to be projected, but not monthly levels of the index. If the price level increases on average by a constant monthly amount, then the end-year value may be inferred from the forecast of the average level (using also the end-period level from the pre-forecast year). However, it is more likely that the rate of inflation is constant during the year than the incremental change in the price level. Of course, the rate of inflation may vary during the year, being faster in some months and slower in others, even after one adjusts the series for the average seasonal pattern. For this reason, the estimate of the average level that is based on end-year values will not be as accurate as the mean of actual monthly levels. If inflation is low, it will not matter much how one calculates the annual average level, or how one infers the end-period value for the forecast year. Nevertheless, if only the end-period values are known and it is desirable to estimate an annual average (or the other way around), the assumption of a constant inflation rate during the period (seasonally adjusted) suggests that the arithmetic mean of end-period values is not the most accurate method.

The general argument is illustrated in Figure 6. A. 1, below. In the diagram, Pt-1 is the value of the price index at the “end” (December) of the preceding year, and Pt is the value at the end of year t. If prices increase by a constant increment, the path of the price level during the year would be as indicated by the dotted line in Figure 6.A. 1. In this case the average level for year t would appropriately be calculated as the arithmetic mean of Pt-1 and Pt yielding the distance from the horizontal axis to point a.

This assumption is not neutral, however. The dotted line in Figure 6.A. 1 actually implies that the inflation rate slows somewhat during the year: the absolute increase in the level is constant, but the price level itself is increasing, so that the proportional change in the level is gradually declining during the year. If, instead, the inflation rate is constant, the path of the price level during the year will be curved upward, like the solid line in Figure 6.A. 1. In this case, a overstates the average level of prices.4

Figure 6. A1 TurkeyThe Time Path of the Price Level During the Year and Calculations of the Yearly Average Level

The distance from the horizontal axis to point g suggests itself as an alternative, and can be calculated from the end-period data,5 but it will be an underestimate of the arithmetic average: the values to the right of g exceed g to a greater extent than values to the left of g fall below it. The distance to g is the level of prices at mid-year and is less than the arithmetic mean of monthly price levels.

The correct value is given by conceptually summing over the instantaneous values of the price level during the year and dividing by the lapse of time. The result, which requires some calculus, is given by6

where Pt is the average level, and Pt and Pt-1 are end-year levels as already defined.

If the inflation rate during the year is constant, the arithmetic mean of the monthly values of P occurring during the year will lie between the arithmetic and geometric means of the successive end-year values. Both of the latter are approximations to the average annual level, but the expression given in equation (6.A. 1) is correct and will in general be a better approximation. Since inflation rates in Turkey have been high in recent years, this latter method will result in increased accuracy.

Equation (6.A. 1) is particularly useful in a financial programming exercise because it makes it possible to deduce the implied rate of inflation during the forecast year. This is quite useful if a program scenario specifies a substantial slowing of the average rate. The implications for inflation during the forecast year will generally be stronger than for the deceleration in the average rate. It may also be used to calculate the level of the nominal exchange rate at the end of the forecast year. Indeed, the method may also be applied to produce more accurate average-period values for debt, the money supply, international reserves, credit, and other stocks of assets and liabilities.


This is determined by banking regulations that specify the dates when banks must satisfy the legal minimum requirements for stocks of reserve assets relative to deposit liabilities.


For banking data, a more accurate average is based on monthly figures for December through December, the mean of thirteen values, since banking series are more nearly end-month data.


cJanuary price levels is a better measure of the end-year price level if the procedures for the collection of data imply that the monthly levels actually refer to mid-months. Similarly, the mean of the average for December of year t-1 and December of year t and the average for January of years t-1 and t is a better measure of the yearly level than the mean of the January and December levels from year t. The numerical consequences of such a refinement are, however, likely to be small.


The inflation rate is usually expressed in terms of percentage change. If Pt,i is the price level in month i of year t, the inflation rate in that month is given by [(Pt,i-Pt,i-1)/Pt,i-1].100.


The distance from the horizontal axis to point g is the geometric mean of the end-period values, calculated as (Pt-1Pt)½ = exp([ln (Pt-1) + ln(Pt)]/2).


In continuous time, the path of the price level can be represented by the expression, Pt = keαt. Integrating this expression, one obtains

Evaluating the area under the curve from t0 (end-of-year t-1) to t1 (end-of-year t) yields

Dividing by t1-t0 to calculate the mean yields P1P0α(t1t0). Using the identity, In (Pt) = ln (keαt) = ln (k)


+ αt, one may add and subtract In (k) in the denominator to obtain,

For n discrete time intervals (for example, 12 months), the precise expression can be shown, using the formula for a finite geometric series, to be P1P0(r1)/nr where r is the nth root of P1/P0, which is the (r - 1 )/nr through-the-year inflation rate (divided by 100) plus unity; P0 is the price level of the time interval preceding the n periods (for example, December of year t-1); and P1 is the price level in the nth period (December of t).

Help with this proof from Abdelhak Senhadji is gratefully acknowledged.


The time series used in these workshops are defined in the data appendix, the final section of this volume. Sources, and values starting in 1979, are given there.


In this volume, all references to logrithms (“logs”) are to “natural” logrithms (logs to the base e, where e = 2,71828…).


The solid line in Figure 6.1 appears to be straight, but it is actually a slight curve, concave from above. This is consistent with the trend equation, which is linear in logs and exponential in antilogs.


As with other sets of regression results presented in these workshops, one purpose is to provide alternative forecasting tools for application to the exercises presented at the end of each chapter. A second purpose is to illustrate the process of experimentation that one might go through in devising a basic econometric specification for the relationship of interest in the context of classical regression analysis. (Time series methods generally exceed the data resources available for Turkey.) As is self-evident in Table 6.1, and later instances as well, the first efforts at estimation in each set involve simpler specifications; subsequent equations typically provide a more complete explanation of variation in the dependent variable, and are usually more satisfactory for forecasting purposes. In some cases the regressions are meant to provide no more than a starting point for forecasting; knowledge of special developments or influences are to be incorporated judgmentally or through supplementary calculations.


For some sectors, the reforms continued for several years. Regression data samples presented in the fiscal and external sector chapters of this volume begin in 1984 or 1985 in most cases.


The Durbin-Watson statistic is biased towards 2.0 for an equation containing a lagged dependent variable. In this case it doesn’t matter since, despite the bias, there is a significant indication of autocorrelation.


Taxation of interest income for enterprises occurred during the 1980s and is to be resumed in 1997, although the methods of collecting this tax are not well known.


Higher real interest rates tend to induce consumers to save more. In this case, however, the interest rate variable is a proxy for interest income received.


The specification of a consumption function that includes the interest rate as an argument is developed explicitly in Appendix I to this chapter


Turkish national accounts data do not provide a disaggregation of gross fixed investment into government and private components. For this equation, a series for government investment expenditure, deflated by the implicit deflator for total investment, was ∏ced together from the sequence of historical IMF country reports. It is not certain that the series constructed in this way is consistent since the concept of investment used in the fiscal accounts may have been revised from time to time.


A study by Ercan Uygur suggests these fairly robust results may be due partly to the influence of investment in housing, which in turn may be influenced in some periods by government subsidies. See “Financial Liberalization and Financial Performance in Turkey,” in Yaman Asikoglu and Hasan Ersel, Financial Liberalization in Turkey (Ankara: Centra Bank of the Republic of Turkey, 1993).


Division by 521.07 causes PM to have the value 100 for the years 1984-86 on average (as does the series PM_D; see the data appendix).


It will hold exactly if one writes (where g denotes the real growth rate).


Exports are an exception because, arguably, export prices are determined in world markets.


It is theoretically possible for the prices of domestically produced investment goods, for example, to rise very fast while the prices of domestically produced consumer goods rise slowly; it is not necessarily true that the same rate of inflation applies to all broad types of domestically produced value added. However, given competition among producers, wage levels and interest rates will tend to be similar across industries, other things being equal, in the typical case. Cost increases will therefore be similar for all producers, especially in a high-inflation economy. Thus, the relation will tend to hold.


The equations in Section f are not appropriate for this purpose. The identities presented there require a forecast of the change in the CDP deflator as an input.

    Other Resources Citing This Publication